The Nekrasov Conjecture for Toric Surfaces

Abstract

The Nekrasov conjecture predicts a relation between the partition function for N=2 supersymmetric Yang-Mills theory and the Seiberg-Witten prepotential. For instantons on R^4, the conjecture was proved, independently and using different methods, by Nekrasov-Okounkov, Nakajima-Yoshioka, and Braverman-Etingof. We prove a generalized version of the conjecture for instantons on noncompact toric surfaces.

38 pages; typos corrected, references added, minor changes (e.g. minor change of convention in Definition 5.13, 5.19, 6.5)

References in corpus (2)

• Instanton counting via affine Lie algebras I: Equivariant J-functions of (affine) flag manifolds and Whittaker vectors
• Random partitions and instanton counting

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• Moduli of framed sheaves on projective surfaces
• N=2 quiver gauge theories on A-type ALE spaces
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• Transversally Elliptic Complex and Cohomological Field Theory
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• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• Beta-ensembles for toric orbifold partition function
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• Deformation-obstruction theory for diagrams of algebras and applications to geometry
• Cohomological Localization of $\mathcal{N}=2$ Gauge Theories with Matter
• Classical deformations of noncompact surfaces and their moduli of instantons
• Noncommutative Instantons in Diverse Dimensions
• S-duality and supersymmetry on curved manifolds
• Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces
• On Framed Quivers, BPS Invariants and Defects
• Symplectic structures on moduli spaces of framed sheaves on surfaces
• The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories
• Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces
• Instanton counting on Hirzebruch surfaces
• Quantum Black Holes, Elliptic Genera and Spectral Partition Functions